Abstract
The purpose of this paper is to study the realization theory of quantum linear systems. It is shown that for a general quantum linear system its controllability and observability are equivalent and they can be checked by means of a simple matrix rank condition. Based on controllability and observability a specific realization is proposed for general quantum linear systems in which an uncontrollable and unobservable subspace is identified. When restricted to the passive case, it is found that a realization is minimal if and only if it is Hurwitz stable. Computational methods are proposed to find the cardinality of minimal realizations of a quantum linear passive system. It is found that the transfer function G(s) of a quantum linear passive system can be written as a fractional form in terms of a matrix function Σ(s); moreover, G(s) is lossless bounded real if and only if Σ(s) is lossless positive real. A type of realization for multiinput–multioutput quantum linear passive systems is derived, which is related to its controllability and observability decomposition. Two realizations, namely the independentoscillator realization and the chainmode realization, are proposed for singleinput–singleoutput quantum linear passive systems, and it is shown that under the assumption of minimal realization, the independentoscillator realization is unique, and these two realizations are related to the lossless positive real matrix function Σ(s). Document embargo till 24/06/2016.
Original language  English 

Pages (fromto)  139151 
Number of pages  13 
Journal  Automatica 
Volume  59 
Early online date  24 Jun 2015 
DOIs  
Publication status  Published  30 Sept 2015 
Keywords
 quantum linear systems
 realization theory
 controllability
 observability
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John Gough
 Faculty of Business and Physcial Sciences, Department of Physics  Personal Chair
Person: Teaching And Research